5 Steps to Analyze Increasing and Decreasing Intervals of a Function

5 steps for finding increasing/decreasing intervals:

When analyzing the increasing or decreasing intervals of a function, here are 5 steps you can follow:

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When analyzing the increasing or decreasing intervals of a function, here are 5 steps you can follow:

1. Identify the function: Start by identifying the given function that you want to analyze. Let’s say the function is f(x).

2. Find the derivative: Take the derivative of the function f(x) with respect to x to find the derivative function f'(x). The derivative represents the rate at which the function is changing at any given point.

3. Solve for critical points: Set the derivative function f'(x) equal to zero or find any points where the derivative is undefined (if any) to identify the critical points. These are the points where the function may change from increasing to decreasing or vice versa.

4. Determine the sign of the derivative: Choose a value to the left and right of each critical point and plug it into the derivative function f'(x). Evaluate whether the values are positive or negative. This will help you determine the sign of the derivative for different intervals.

5. Analyze increasing/decreasing intervals: Based on the signs of the derivative, you can identify the intervals where the function is increasing or decreasing:

– If the derivative is positive in an interval, it means the function is increasing in that interval.

– If the derivative is negative in an interval, it means the function is decreasing in that interval.

– If the derivative equals zero at a point, it means that point is a potential maximum or minimum.

By following these steps, you can analyze the increasing and decreasing intervals of a given function.

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